Casino Size and Revenue Use the same paired data from the prec...

Question

Casino Size and Revenue Use the same paired data from the preceding exercise.

b. What is the best predicted amount of revenue for a casino with a size of 200 thousand square feet? Is it likely that the best predicted amount of revenue will be accurate?

Accepted Answer

Welcome back, everyone. A city planning department conducted a regression analysis to explore the relationship between the number of hotel rooms in a resort and the annual revenue generated in millions of dollars. The regression equation obtained from the data of five resorts revenue equals 2.0 plus 0.5 multiplied by rooms. Number 1, what is the best predicted annual revenue for a resort that has 100 rooms? Let's begin with the first part of this problem, and we're going to use the equation of the regression line revenue. is equal to 2.0 plus 0.5 multiplied by the number of rooms and we're given 100 rooms, so we're multiplying by 100. 2 + 0.5 multiplied by 100, gives us 52, and we know that revenue is measured in millions of dollars, meaning the answer to this part would be $52 million. Now part two says based on the regression model, do you think this prediction is likely to be accurate? So for part two, first of all, let's understand what range we used to produce this regression line. The lowest value is 50, and the highest one is 90, so the range used was between 50 and 90 rooms. Ideally, whenever we are using a regression line, we want to ensure that the independent variable in this case 100 is within the range. Now 100 is slightly outside of the range, right, because it's greater than the upper bound of 90. However, we have to be reasonable because it is only slightly beyond the range, so. We can say that based on the regression model, this prediction is likely to be accurate or simply yes, because The prediction. Yes Only Slightly Beyond the range. And We can also see that. For 100 rooms we got $52 million in revenue, right? Our trend, as we can see, corresponds to an increase in revenue with an increase in rooms. So for 90 rooms we had an estimated revenue of 47, and now for 100 rooms we expect a larger number, so 52 is higher than 47, right, meaning we can also include that. It follows the trend. So follows. That trend And that would be our answer. So for part one, we got a revenue of $52 million. For part two, we have a conclusion that this prediction is likely to be accurate because it is only slightly outside of the range and it follows the trend. Thank you for watching.

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Casino Size and Revenue Use the same paired data from the preceding exercise.
b. What is the best predicted amount of revenue for a casino with a size of 200 thousand square feet? Is it likely that the best predicted amount of revenue will be accurate?

Key Concepts

Linear Regression

Prediction Interval

Correlation

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Casino Size and Revenue Use the same paired data from the preceding exercise.b. What is the best predicted amount of revenue for a casino with a size of 200 thousand square feet? Is it likely that the best predicted amount of revenue will be accurate?